{"paper":{"title":"Remarks on two fourth order elliptic problems in whole space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Baishun Lai, Dong Ye","submitted_at":"2014-01-17T16:23:36Z","abstract_excerpt":"We are interested in entire solutions for the semilinear biharmonic equation $\\Delta^{2}u=f(u)$ in $\\R^N$, where $f(u)=e^{u}$ or $-u^{-p}\\ (p>0)$. For the exponential case, we prove that any classical entire solution verifies $-\\Delta u>0$ without any restriction, which completes the results in \\cite{Dupaigne, xu-wei} and yields a nonexistence result in $\\R^2$ ; we obtain also a refined asymptotic expansion of radial separatrix solution for $N=3$, which answers a question in \\cite{Berchio}. For the negative power case, we show the nonexistence of the classical entire solution for any $0<p\\leq1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4400","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}